Embedding theorems for functional spaces associated with a class of Hermitian forms
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 10 (2017) no. 1, pp. 83-95.

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We prove embedding theorems into the scale of Sobolev–Slobodetskii spaces for functional spaces associated with a class of Hermitian forms. More precisely we consider the Hermitian forms constructed with the use of the first order differential matrix operators with injective principal symbol. The results are valid for both coercive and non-coercive forms.
Keywords: non-coercive Hermitian forms, embedding theorems, matrix elliptic operators.
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Anastasiya S. Peicheva. Embedding theorems for functional spaces associated with a class of Hermitian forms. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 10 (2017) no. 1, pp. 83-95. http://geodesic.mathdoc.fr/item/JSFU_2017_10_1_a12/

[1] S. L. Sobolev, Some applications of functional analysis in mathematical physics, scientific. ed., Nauka, M., 1988 (in Russian)

[2] O. A. Ladyzhenskaya, N. N. Uraltseva, Linear and quasi-linear elliptic equations, Nauka, M., 1973 (in Russian)

[3] J. L. Lions, Non-Homogeneous Boundary Value Problems and Applications, v. 1, Springer-Verlag, Berlin–Heidelberg–New York, 1972

[4] M. I. Vishik, “About strongly elliptic systems of differential equations”, Mat. sb., 29(71):3 (1951) (in Russian) | MR | Zbl

[5] M. S. Agranovich, “Mixed problems in Lipschitz domains for strongly elliptic systems of 2nd order”, Funks. analiz i ego pril., 45:2 (2011), 1–22 (in Russian) | DOI | MR | Zbl

[6] M. S. Agranovich, “Spectral Problems in Lipschitz Domains”, Sovr. probl. mat. Fundament. naprav., 39 (2011), 11–35 (in Russian) | MR

[7] L. N. Slobodeckii, “The generalized Sobolev spaces and their application to boundary value problems for differential equations in partial derivatives”, Uch. zap. Leningr. gos. ped. inst., 197 (1958), 54–112 (in Russian) | MR

[8] N. N. Tarkhanov, The Cauchy problem for solutions of elliptic equations, v. 7, Acad. Verl., Berlin, 1995 | MR

[9] K. Yoshida, Functional analysis, Springer-Verlag, 1965 | MR

[10] A. A. Shlapunov, N. N. Tarkhanov, “The Sturm-Liouville problems in weighted spaces in domains with smooth edges. I”, Siberian Advances in Mathematics, 26:1 (2016), 30–76 | DOI | MR

[11] M. Schechter, “Negative norms and boundary problems”, Ann. Math., 72:3 (1960), 581–593 | DOI | MR | Zbl

[12] B.-W. Schulze, A. A. Shlapunov, N. N. Tarkhanov, “Green integrals on manifolds with cracks”, Annals of Global Analysis and Geometry, 24 (2003), 131–160 | DOI | MR | Zbl

[13] A. A. Shlapunov, N. N. Tarkhanov, “Duality by reproducing kernels”, Int. J. of Math. and Math. Sc., 6 (2003), 327–395 | DOI | MR | Zbl

[14] A. S. Peycheva, A. A. Shapunov, “On the completeness of root functions of Sturm-Liouville problems for the Lame system in weighted spaces”, ZAMM (Z. Angew. Math. Mech.), 95:11 (2015), 1202–1214 | DOI | MR

[15] A. A. Shlapunov, “Spectral decomposition of Green's integrals and existence of $W^{s,2}$-solutions of matrix factorizations of the Laplace operator in a ball”, Rend. Sem. Mat. Univ. Padova, 96 (1996), 237–256 | MR | Zbl

[16] A. Polkovnikov, A. Shlapunov, “On the spectral properties of a non-coercive mixed problem associated with $\overline \partial$-operator”, J. Siberian Fed. Univ., Math. and Phys., 6:2 (2013), 247–261